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On line solution of multivariate equations：
    First set the elements of the equation (i.e. the number of unknowns), then click the "Next" button to enter the coefficients of each element of the equation set, and click the "Next" button to obtain the solution of the equation set.
    Note that the coefficients of each element of the equation system can only be numbers, not algebraic expressions (including mathematical functions).
    Current location：Equations > Multivariate equations > Answer
detailed information：
The input equation set is:
 160A + 250B + 300C + 600D = 3128508    (1)
 A + B + C + D = 12126    (2)
 A + 2B = 5010    (3)
 A = 2100    (4)
Question solving process:

Divide the two sides of equation (1) by 160, the equation can be obtained:
         A + 
25
16
B + 
15
8
C + 
15
4
D = 
782127
40
    (5)
, then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
 160A + 250B + 300C + 600D = 3128508    (1)
- 
9
16
B - 
7
8
C - 
11
4
D = - 
297087
40
    (2)
 A + 2B = 5010    (3)
 A = 2100    (4)

Divide the two sides of equation (1) by 160, the equation can be obtained:
         A + 
25
16
B + 
15
8
C + 
15
4
D = 
782127
40
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 160A + 250B + 300C + 600D = 3128508    (1)
- 
9
16
B - 
7
8
C - 
11
4
D = - 
297087
40
    (2)
 
7
16
B - 
15
8
C - 
15
4
D = - 
581727
40
    (3)
 A = 2100    (4)

Divide the two sides of equation (1) by 160, the equation can be obtained:
         A + 
25
16
B + 
15
8
C + 
15
4
D = 
782127
40
    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 160A + 250B + 300C + 600D = 3128508    (1)
- 
9
16
B - 
7
8
C - 
11
4
D = - 
297087
40
    (2)
 
7
16
B - 
15
8
C - 
15
4
D = - 
581727
40
    (3)
- 
25
16
B - 
15
8
C - 
15
4
D = - 
698127
40
    (4)

Multiply both sides of equation (2) by 7
Divide the two sides of equation (2) by 9, the equation can be obtained:
        - 
7
16
B - 
49
72
C - 
77
36
D = - 
693203
120
    (8)
, then add the two sides of equation (8) to both sides of equation (3), the equations are reduced to:
 160A + 250B + 300C + 600D = 3128508    (1)
- 
9
16
B - 
7
8
C - 
11
4
D = - 
297087
40
    (2)
- 
23
9
C - 
53
9
D = - 
304798
15
    (3)
- 
25
16
B - 
15
8
C - 
15
4
D = - 
698127
40
    (4)

Multiply both sides of equation (2) by 25
Divide the two sides of equation (2) by 9, the equation can be obtained:
        - 
25
16
B - 
175
72
C - 
275
36
D = - 
495145
24
    (9)
, then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
 160A + 250B + 300C + 600D = 3128508    (1)
- 
9
16
B - 
7
8
C - 
11
4
D = - 
297087
40
    (2)
- 
23
9
C - 
53
9
D = - 
304798
15
    (3)
 
5
9
C + 
35
9
D = 
47668
15
    (4)

Multiply both sides of equation (3) by 5
Divide the two sides of equation (3) by 23, the equation can be obtained:
        - 
5
9
C - 
265
207
D = - 
304798
69
    (10)
, then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
 160A + 250B + 300C + 600D = 3128508    (1)
- 
9
16
B - 
7
8
C - 
11
4
D = - 
297087
40
    (2)
- 
23
9
C - 
53
9
D = - 
304798
15
    (3)
 
60
23
D = - 
142542
115
    (4)

Multiply both sides of equation (4) by 1219
Divide both sides of equation (4) by 540, get the equation：
         
53
9
D = - 
419707
150
    (11)
, then add the two sides of equation (11) to both sides of equation (3), get the equation：
 160A + 250B + 300C + 600D = 3128508    (1)
- 
9
16
B - 
7
8
C - 
11
4
D = - 
297087
40
    (2)
- 
23
9
C = - 
3467687
150
    (3)
 
60
23
D = - 
142542
115
    (4)

Multiply both sides of equation (4) by 253
Divide both sides of equation (4) by 240, get the equation：
         
11
4
D = - 
261327
200
    (12)
, then add the two sides of equation (12) to both sides of equation (2), get the equation：
 160A + 250B + 300C + 600D = 3128508    (1)
- 
9
16
B - 
7
8
C = - 
873381
100
    (2)
- 
23
9
C = - 
3467687
150
    (3)
 
60
23
D = - 
142542
115
    (4)

Multiply both sides of equation (4) by 230, get the equation：
         600D = -285084    (13)
, then subtract both sides of equation (13) from both sides of equation (1), get the equation：
 160A + 250B + 300C = 3413592    (1)
- 
9
16
B - 
7
8
C = - 
873381
100
    (2)
- 
23
9
C = - 
3467687
150
    (3)
 
60
23
D = - 
142542
115
    (4)

Multiply both sides of equation (3) by 63
Divide both sides of equation (3) by 184, get the equation：
        - 
7
8
C = - 
3166149
400
    (14)
, then subtract both sides of equation (14) from both sides of equation (2), get the equation：
 160A + 250B + 300C = 3413592    (1)
- 
9
16
B = - 
13095
16
    (2)
- 
23
9
C = - 
3467687
150
    (3)
 D = - 
23757
50
    (4)

Multiply both sides of equation (3) by 2700
Divide both sides of equation (3) by 23, get the equation：
        -300C = -2713842    (15)
, then add the two sides of equation (15) to both sides of equation (1), get the equation：
 160A + 250B = 699750    (1)
- 
9
16
B = - 
13095
16
    (2)
- 
23
9
C = - 
3467687
150
    (3)
 D = - 
23757
50
    (4)

Multiply both sides of equation (2) by 4000
Divide both sides of equation (2) by 9, get the equation：
        -250B = -363750    (16)
, then add the two sides of equation (16) to both sides of equation (1), get the equation：
 160A = 336000    (1)
- 
9
16
B = - 
13095
16
    (2)
 C = 
452307
50
    (3)
 D = - 
23757
50
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 2100    (1)
 B = 1455    (2)
 C = 
452307
50
    (3)
 D = - 
23757
50
    (4)


Therefore, the solution of the equation set is:
A = 2100
B = 1455
C = 
452307
50
D = - 
23757
50


Convert the solution of the equation set to decimals:
A = 2100
B = 1455
C = 9046.140000
D = -475.140000

解方程组的详细方法请参阅：《多元一次方程组的解法》
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